The generator matrix

 1  0  0  0  0  1  1  1  2  1  1  1  X  1  2  2  1  X  1 X+2  1  1  1  1  1  1 X+2  1  X X+2  0 X+2  0 X+2  2  2  0  X  1  1  X  1 X+2  1  1  X  1  1
 0  1  0  0  0  0  2  0  2  0  2  2  2  0  2  0 X+1  1 X+3  1  1 X+1  1 X+3 X+1  3  1 X+2  1 X+2  1  X  1  1 X+2 X+2  1 X+2  3  X  1  X  1  1  1  1 X+3  X
 0  0  1  0  0  0  3  1  1  2  0 X+1  1  1  1 X+2 X+1  0 X+2  0 X+1  X  2 X+3  1 X+2  X  0 X+1  1 X+1  1 X+1  2  1  1 X+1  X  1 X+1 X+3  1 X+2 X+2  2  X  2  0
 0  0  0  1  0  1  1  2  1 X+2 X+1 X+3  0 X+2 X+1  1 X+2  3  0  3 X+1 X+1  1  2 X+3  2 X+2  3  X X+2  2  3  1 X+1  3  2 X+1  1 X+3  3  2  X  2 X+3  X  3 X+3  X
 0  0  0  0  1  1  2  3  1  1  X  1  1  2 X+2  1  3  0  X X+1 X+2  0 X+1  X  1 X+1  3  1 X+1  0  X  3 X+2  1 X+3 X+3 X+1  2 X+1 X+3 X+1 X+1  0  2  3  1 X+3 X+1
 0  0  0  0  0  2  0  0  0  0  2  2  2  2  2  2  2  2  2  0  2  0  2  0  0  0  2  0  0  2  2  0  0  0  2  0  2  2  2  0  2  0  0  2  2  0  2  2

generates a code of length 48 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 39.

Homogenous weight enumerator: w(x)=1x^0+164x^39+555x^40+1272x^41+1886x^42+2890x^43+3863x^44+5212x^45+5907x^46+7234x^47+7152x^48+7306x^49+6399x^50+5618x^51+3623x^52+2866x^53+1713x^54+986x^55+522x^56+198x^57+90x^58+36x^59+26x^60+10x^61+4x^62+2x^64+1x^74

The gray image is a code over GF(2) with n=192, k=16 and d=78.
This code was found by Heurico 1.13 in 41 seconds.